Solidification process of polymer melts represents multidimensional interactions of non-linear processes, which take place on different time-space scales. The Study of complex interactions (The Science of Complexity) represents one of the most rapidly developing scientific areas. This field is inherently interdisciplinary; it combines almost all classical disciplines of science. The most courageous expect that research in this field might lead to the understanding of how the life on earth has evolved. Initiation of the research goes back to 1999, when Toyota company published surprising results of discovery that 1-2 vol. % of the nano-particles added to the polyamide resulted in an extraordinary improvement of the material mechanical properties. Technological breakthrough of our research group, which resulted from the collaboration with BASF, brings Slovenia among the leaders in the field of new generation nano-structured polymers and corresponding technologies. Intensive continuation of this research and implementation of the results into industrial applications may lead to a mayor techno-economical breakthrough comparable to the success story of Nokia in Finland. Research in this field is one of the priorities of the EU 6FP, and of the American National Research Program: NNI-National Nanotechnology Initiative, published in June 2002.